Lars E.O. Svensson
Princeton University, CEPR, and NBER
University of Wisconsin and NBER
First draft: May 2005
This version: May 2007
We examine optimal and other monetary policies in a linear-quadratic setup with a relatively general form of model uncertainty, so-called Markov jump-linear-quadratic systems extended to allow forward-looking variables. The form of model uncertainty our framework encompasses includes: simple i.i.d. model deviations; serially correlated model deviations; estimable regime-switching models; more complex structural uncertainty about very different models, for instance, backward- and forward-looking models; time-varying central-bank judgment about the state of model uncertainty; and so forth. We provide an algorithm for finding the optimal policy as well as solutions for arbitrary policy functions. This allows us to compute and plot consistent distribution forecasts – fan charts – of target variables and instruments. Our methods hence extend certainty equivalence and “mean forecast targeting” to more general certainty non-equivalence and “distribution forecast targeting.”
JEL Classification: E42, E52, E58
Keywords: Optimal policy, multiplicative uncertainty
Programs by Satoru Shimizu, Lars E.O. Svensson, and Noah Williams
Last update: July 25, 2007
The main programs are opt_policy.m and
which compute optimal policy and the simulated distribution of impulse
responses under the optimal policy. They require that a user define a
model as a structured variable consisting of a collection of matrices.
Given a specification of appropriate matrices, set_up_model.m defines the structured variable appropriately.
Two examples of how to use the programs to reproduce the results in the DFT paper are given in the following:
These programs also provide much more detail on the setup and structure of the models and algorithms.
In a bit more detail, the other files consist of the following:
Also included are two utility files from Lars Peter Hansen and Thomas J. Sargent that accompany their monograph
Recursive Models of Dynamic Linear Economies